Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C4⋊(C59⋊C8) | C2 | semidirect |
| 3. #21422871 | C2 | semidirect |
| 6. #21421992 | C2 | semidirect |
| 7. C59×#1276 | C2 | semidirect |
| 17. #16837147 | C4 | semidirect |
| 18. #16837145 | C4 | semidirect |
| 156. #1276 | D59 | semidirect |
| 178. C59 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424924 | 2 |
| C4×C4⋊(C59⋊C8) | 2 |
| #21422871 | 2 |
| #21422743 | 2 |
| #21422496 | 2 |
| #21421992 | 2 |
| C59×#1276 | 2 |
| #9577 | 59 |